SECTION XX.

COEFFICIENT OF INCREASE OF PRESSURE OF A GAS WITH TEMPERATURE.

Apparatus required: Bulb and pressure apparatus, water bath, thermometer.

If the temperature of a constant volume of gas is raised, the pressure of the gas varies according to the equation Pt = Po (1 + ẞt), where p. is the pressure at 0° C., t the temperature Centigrade, and B a constant, called the coefficient of increase of pressure with temperature.

B

A

w

Fig. 38.

To verify the law expressed by the above equation in the case of air the apparatus shewn in Fig. 38 is provided.

A is a glass bulb to which a bent tube of small bore BCD is attached. At the lowest point of the tube it branches and

to the branch is attached a piece of rubber tubing which can be compressed between the plate E and the stand by turning

a screw.

The rubber tube and the lower part of the tube CD are filled with mercury, and the open end of the rubber tube then closed by a short glass rod.

By adjusting the quantity of mercury and the pressure at E the surface of the mercury in the left-hand tube may be brought to the fixed mark C. If the position of the surface of the mercury in D is then read, and the height of the barometer is known, we have the total pressure to which the air in A is subjected.

To determine how this pressure varies with the temperature of the air in the bulb, fill the bath in which the bulb is placed with cold water, noting its temperature. Adjust the mercury to C, and read the position of D on the scale alongside.

Raise the temperature of the bath about 5° C. keeping the water stirred, and repeat the adjustment and readings. Take four observations at intervals of 5° C. and then wait until the thermometer has risen 25°, i.e. stands 40° higher than at the beginning of the observations. Take four more observations at intervals of 5°. Then release the pressure of the screw so as to lower the mercury in the tube C and prevent it running back into the bulb as the air in the bulb is cooled, and pour sufficient cold water into the bath to lower its temperature 5° C. Stir well and raise the mercury to C again, then read D. Lower the mercury, cool further and repeat the observations till the original temperature is reached. Take the means of each pair of observations at nearly the same temperature and use them in what follows.

Read the barometer; the pressure of the gas in terms of a column of mercury will be the sum of the height of the barometer and the difference in level between C and D.

If p is this pressure and v the volume of the gas at temperature t, we have pv povo (1+ẞt), where v, is the volume. at 0° C.

The volume of the containing vessel will increase slightly as the temperature rises owing to the expansion of the glass.

If the coefficient of expansion of the glass is a, the volume v of the vessel is obtained from v = v。 (1+at).

Or since in the above experiments at is always less than '002 and Bt less than 2, we may write with an accessory of 1 part in 2000

If pit1, pat, are two sets of readings of p and t, we may form two similar equations and eliminating p, find

B may therefore be calculated, if a is known, by observation of any two corresponding pressures and temperatures. If a number of readings are taken at regular intervals of temperature we may apply the method explained in Section (III) and secure the smallest probable error by taking a certain number of observations, omitting the same number, and finally taking again an equal number. The observations are combined and reduced as given in the Table below. Of the two forms for (Ba) given above the first involves less arithmetical labour, and would naturally be used in case the pressure is observed for only two temperatures. But for a series of experiments the results may be tabulated in a more symmetrical manner if the second form is adopted. The labour of calculation is reduced if the reciprocals of p1 and p2 are obtained from Barlow's Tables.

The fractions t/p2 etc. and the final quotients may be found with sufficient accuracy from Crelle's multiplication tables. Arrange the observations as follows:

According to Regnault should be equal to 003669. There are two further sources of error which tend to reduce the apparent value of B. One is the expansion of the glass vessel due to increased internal pressure at the higher temperatures, and the other is due to the air in the tube leading from the bulb not being at the same temperature as that in the bulb. The first-named error is not likely to be more than 1 in 300,000 with the dimension of apparatus used, the second error will not exceed 1 in 6000 if the bulb has a diameter of 10 cms., and the length of capillary tube between the bulb and the fixed mark is not more than 20 cms. and its diameter not more than 18 mm.

If the interior of bulb is not thoroughly dry too high value will be obtained owing to the evaporation of the water from the walls of the vessel. To secure dryness a few drops of strong sulphuric acid are introduced into the bulb before the mercury is poured into the tube.

The increase of pressure of a gas is used to measure temperatures in the "constant volume gas thermometers," the construction of which is the same in principle as that of the apparatus used in this exercise.

SECTION XXI.

COEFFICIENT OF EXPANSION OF AIR AT

CONSTANT PRESSURE.

Apparatus required: Graduated tube and index, water bath, and thermometer.

When the temperature of a gas maintained at constant pressure is raised, the volume increases, and may be represented by an expression of the form.

v=vo (1+at),

where v is the volume at t°C., v。 at 0°C. and a is a constant called the coefficient of expansion of the gas.

If the gas is enclosed in a vessel the coefficient of cubical expansion of the material of which is B, the apparent volume of the gas will for expansions not greater than 30 per cent. be expressed with an accuracy of 1 part in 2000 by the equation

If t, and to are two temperatures and v1, v, the corresponding apparent volumes, it is found on eliminating v, that

Hence if observations of the variation of volume of a given mass of gas, enclosed in a vessel of known coefficient of expansion, are made, the coefficient of expansion of the gas may be determined.

The apparatus provided consists of a graduated glass tube of fine bore, one end of which is sealed, and the other attached